1. Field of the Invention
The present invention relates to a method for analyzing an electroencephalogram(EEG) using a correlation dimension, and more particularly to a method for analyzing an EEG time series by which a brain state can be determined using a time-delay determining method necessary for reconstructing vectors from the EEG time series in the embedding dimension, and a relative ratio of a correlation exponent(hereinafter, referred to as a relative correlation exponent).
2. Description of the Conventional Art
It is well known that a correlation dimension is most widely used in chaotic dynamics analyses. In analyzing the EEG(electroencephalogram) through the use of the conventional correlation dimension, the analysis method includes a first step of constructing vectors in an embedding dimension from the EEG time series by using a time delay, a second step of calculating a correlation integral for the vectors, a third step of obtaining a correlation exponent by using the local slope of the correlation integral, and a fourth step of obtaining the correlation dimension from the correlation exponent with varying the embedding dimension. For the stochastic time series, the correlation exponent continuously increases with the embedding dimension. In case of the chaotic system, the correlation exponent converges into a constant value which is referred to as the correlation dimension. Accordingly, the measurement of the correlation dimension enables one to determine whether the time series is stochastic or chaotic. Also, since the correlation dimension for the EEG during sleep and epileptic seizure is much lower than that of the normal brain state, the correlation dimension can be used in diagnosing the encephalopathy.
However, since the conventional correlation dimension measurement includes the above first step of obtaining the time delay from the specific function, such as the autocorrelation function, the dependence on the time delay of the embedding dimension is ignored. Further, at the fourth step in the above-mentioned method, it is difficult to obtain the correlation exponent in a high embedding dimension, because the number of data of the EEG time series is limited in experiments.